Question

The concentration of a drug in the body fluids is given by C = Coe-0.81, where Co is the initial dosage and t is the time in hours elapsed after administering the dose.85 mg of a drug is given, how much time elapses until 21 mg of the drug remains? Round your answer to two decimal places, if necessary._____ hours

Answer 1

Given

The equation is given as

$C=C_oe^{-0.8t}$

here C is the remaining dosage and Co is the initial dosage.

Explanation

To find the time elapses until 21 mg of the drug remains.

$\begin{gathered} 21=85e^{-0.8t} \\ 0.2470588=e^{-0.8t} \end{gathered}$

Take ln both sides.

$\begin{gathered} ln\text{ 0.2470588=-0.8tlne} \\ -1.3981289=-0.8t \\ t=\frac{1.3981289}{0.8} \\ t=1.747hrs \end{gathered}$

Answer

Hence the time elapses until 21 mg of the drug remains is 1.747 hours.